RC circuit differential equations

I need to solve the differential equations of a RC circuit given a voltage and a current pulse. I have to get this responses:

http://i.imagehost.org/view/0340/Respuesta1 [Broken]

I'm using matlab, with runge kutta. I've been solving the equations separately changing the initial conditions and the value of current and voltage, but i want to know if there is a way to get the response solving the differential equations only once??

By the way, the differential equations i'm trying to solve are

[tex]\frac{dV}{dt}=\frac{1}{C}(i(t)-\frac{V}{R})[/tex]

and

[tex]I = \frac{dQ}{dt}=\frac{1}{R}(V-\frac{Q(t)}{C}) [/tex]

How should i solve this equations in order to get the responses showed in the pictures???

I'm not getting this response, and i've checked my program (runge kutta) with a current pulse and works ok... So the only way i'm not getting what i want is that the differential equation i'm solving is wrong. Please, can you tell me the correct equation?? Thanks!!

I'm not getting this response, and i've checked my program (runge kutta) with a current pulse and works ok... So the only way i'm not getting what i want is that the differential equation i'm solving is wrong. Please, can you tell me the correct equation?? Thanks!!

If you drew the circuit you cared about I think we could help. Trying to "reverse engineer" what you are really interested in is a lot to ask!